二次同余根的精细分布

IF 2.3 1区 数学 Q1 MATHEMATICS
Jens Marklof, Matthew Welsh
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引用次数: 2

摘要

我们建立了二次同余μ2≡Dmodm的根在小区间内的分布的极限律,其中d>为无平方数,d 1mod4为无平方数。这是通过将问题转化为双曲平面上某些测地线随机线过程的收敛来实现的。这种几何解释特别允许我们推导出根对相关密度的显式表达式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fine-scale distribution of roots of quadratic congruences
We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence μ2≡Dmodm, with D>0 square-free and D≢1mod4. This is achieved by translating the problem to convergence of certain geodesic random line processes in the hyperbolic plane. This geometric interpretation allows us in particular to derive an explicit expression for the pair correlation density of the roots.
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来源期刊
CiteScore
3.40
自引率
0.00%
发文量
61
审稿时长
6-12 weeks
期刊介绍: Information not localized
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